First off, I'd say never completely rule out periods of silence. Lots of people are perfectly happy to coexist in silence. Yes, it can be awkward too.

Now on to the question. Everyone has interests, passions, hopes, fears. But many people are not very good at opening up about them. I am a prime example. I barely talk at all upon first meeting people, but eventually if the relationship progresses, I won't stop yapping. So the challenge with people like that is finding a way to organically get them to open up.

Now there has been the suggestion ITT to start asking them questions. What is your favorite movie? What sports do you enjoy? That can sometimes work, but often it just feels like an interview and none of the answers really go anywhere. If you try this technique, it is imperative that you actually follow up on these answers. Let their answer be a building block to the conversation, not the dead end which leads to the next interview question.

In my experience the best way to get somebody to open up and lead to meaningful conversations (and friendship if you're into that sort of thing) is doing an activity together. Obviously if you're trying to make small talk while sitting at the airport, this is not going to work well. But if you can, get out there. If you're in school, solve some homework problems together. If you're in the office, work with them on a work assignment. Play some pickup soccer or frisbee in the park. Anything that keeps the mind or body active that you do together, builds a common bond right there. And as the person becomes more comfortable with you, you'll notice the conversation being less and less one sided.